How can my friend re-enter Thailand on a tourist visa after her non-B visa expires?

Someone has an excellent English teacher. You present your situation very well. I hope your situation has a good resolution.

She will go to the Immigration Office at IT Square Lak Si to extend her Visa Exemption.

But since she will leave Thailand on the 31st and be gone for a week she may not get the 45 day Visa Exemption currently going on in the first place, but the regular 30 days. As far as I know it is set to go back to the normal 30 days at the end of March. But extending the stay is at IT Square Lak Si either way.

She is required to have a ticket out of the country before her exemption expires when returning to Thailand. But she may or may not be asked for it.

If she will have problems returning is something I can't really answer.

Is she on the 90 day non-B visa purchased from overseas, or a 1 year extension she got from immigration?

If she is on a 1 year extension, then BEFORE she leaves, she needs to get a letter from her employer stating when her work ends and then go cancel her work permit, then take the cancelled work permit and that letter to immigration to cancel her non-B extension.

If she does not do this, she cannot get a new non-B because she didn't cancel her previous one, and she will be fined 20,000 baht for failing to do so when she stopped working before.

It does not matter if her extension runs out, she is required to cancel it because she signed a document saying she would do so when she got it.

After she does that, she can leave the country and then return and as long as she enters the country BEFORE April 1st, meaning March 31st is the last day, she will be stamped in for 45 days visa exempt (if she is from a visa exempt country). If she enters April 1st or later, she will be stamped in for 30 days visa exempt as the temporary increase to 45 days ends on March 31st. This is not a visa, it is visa exempt, meaning no visa at all.

This can be extended ONE time for an additional 30 days.